To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{81}{36}} \)
\( \frac{\sqrt{81}}{\sqrt{36}} \)
\( \frac{\sqrt{9^2}}{\sqrt{6^2}} \)
\( \frac{9}{6} \)
1\(\frac{1}{2}\)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{2 x 4}{2 x 4} \) - \( \frac{5 x 1}{8 x 1} \)

\( \frac{8}{8} \) - \( \frac{5}{8} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{8 - 5}{8} \) = \( \frac{3}{8} \) = \(\frac{3}{8}\)

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{8} \) ÷ \( \frac{1}{7} \) = \( \frac{2}{8} \) x \( \frac{7}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{8} \) x \( \frac{7}{1} \) = \( \frac{2 x 7}{8 x 1} \) = \( \frac{14}{8} \) = 1\(\frac{3}{4}\)